Problem 180 - Master Resource Book in JEE Main Physics

Question

When you make ice cubes, the entropy of water [UP SEE 2006] (a) does not change (b) increase (c) decreases (d) may either increase or decrease depending on the process used

Step-by-Step Solution

Answer

The entropy of water decreases when you make ice cubes.

Step 1: Understand Entropy

Entropy is a measure of randomness or disorder in a system. Generally, in thermodynamics, when a system becomes more ordered, its entropy decreases, and when it becomes more disordered, its entropy increases.

Step 2: Consider the Process of Freezing

When you make ice cubes, you are turning liquid water (a more disordered state) into solid ice (a more ordered state). The molecules in solid ice are more organized in a crystal lattice compared to the free-moving molecules in liquid water.

Step 3: Apply Entropy Concepts

Since the water molecules are becoming more ordered when forming ice, the entropy of the water decreases. This is a key characteristic of the freezing process.

Step 4: Analyze the Given Options

Based on the understanding of entropy changes during the phase transition from liquid to solid, the correct choice is that the entropy decreases. Therefore, option (c) is the correct answer.

Key Concepts

Phase Transition

When talking about phase transitions, we are referring to the transformation of a substance from one state of matter to another. This includes solid, liquid, and gas states. In thermodynamics, phase transitions are monumental because they involve the absorption or release of energy, which is directly related to entropy changes.

For example, when water freezes into ice, it undergoes a phase transition from liquid to solid. This is a crucial example because it illustrates how entropy decreases when moving from a more disordered state (liquid) to a more ordered state (solid). The molecules in liquid water are chaotic and no longer tied to a particular form. During freezing, they arrange into an organized structure, thereby reducing entropy.

Understanding phase transitions helps us comprehend how energy and disorder are managed in everyday processes, from water boiling to steam or ice melting back to liquid.

Disorder in Systems

Disorder in systems refers to the concept of entropy. Simply put, entropy is the measure of disorder or randomness within a system. In thermodynamic terms, systems tend to move towards a state of higher entropy or disorder unless energy is applied to create order.

Key points to consider about entropy:

• Entropy increases when a solid becomes a liquid or gas, as particles have more freedom to move randomly.
• Entropy decreases when a liquid freezes to become a solid, as particles settle into a structured lattice.
• In closed systems, entropy will increase over time unless energy intervention occurs.

Understanding these aspects of disorder in systems allows us to predict how energy exchanges can result in different properties and states, such as heating, cooling, or melting.

Freezing Process

The freezing process is a wonderful demonstration of how entropy decreases as disorder is transformed into order. Let's explore this in detail.

When water freezes, it undergoes a significant structural change. In the liquid state, water molecules move freely, resulting in a high degree of disorder and large entropy. However, as cooling continues, the molecules lose energy and slow down. Eventually, they bond into a rigid lattice structure forming ice—a highly ordered state with lower entropy.

During this process, energy in the form of heat is released into the environment, further facilitating the rearrangement into the orderly structure. Thus, freezing exemplifies the principles of thermodynamics, demonstrating how energy and disorder play pivotal roles in state transformations.

Comprehending the freezing process helps us understand larger concepts in natural science and daily activities like preserving foods or operating refrigerators.